Costas loop is usually used in navigation receiver as carrier tracking loop, so many analyses have been made about coastas loop. Traditional analysis is based on unitary signal power multiplicative detector, and the loop bandwidth is considered constant no matter what the signal to noise ratio is. In this paper, two kinds of phase detectors are precisely modeled and analyzed. The pll thermal noise formula is given and proved by simulation. If the signal to noise ratio is lower than 4dB, the performances of the two detectors are almost the same, the signal to noise ratio threshold of tracking is almost the same. The results of this paper can be used to design the satellite navigation receiver.